How do you solve #3|2x + -5| + 3 = 42#?

2 Answers

Answer:

#x=9 or x=-4#

Explanation:

Here, #3|2x+(-5)|+3=42,#

Adding #(-3)# both sides

#3|2x+(-5)|+3+(-3)=42+(-3)#

#=>3|2x+(-5)|=39,#

Dividing both sides by 3

#(cancel(3)|2x+(-5)|)/(cancel(3))=39/3=>|2x+(-5)|=13#

#2x+(-5)=13or2x+(-5)=-13#

Adding #5# both sides

#2x+(-5)+5=13+5or2x+(-5)+5=-13+5#

#=>2x=18 or 2x=-8=>x=9 or x=-4#

Mar 18, 2018

Answer:

#x=-4,9#

Explanation:

Solve:

#3abs(2x+ -5)+3=42#

Simplify the absolute value.

#3abs(2x-5)+3=42#

Subtract #3# from both sides of the equation.

#3abs(2x-5)+3-3=42-3#

Simplify.

#3abs(2x-5)+0=39#

#3abs(2x-5)=39#

Divide both sides by #3#.

#(cancel(3)^1abs(2x-5))/cancel(3)^1=cancel39^13/cancel(3)^1#

Simplify.

#abs(2x-5)=13#

Since #abs(+-a)=a#, we can break the equation into two equations:

#2x-5=13# and #-(2x-5)=13#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Solve the first equation:

Add #5# to both sides of the equation.

#2x-5+5=13+5#

Simplify.

#2x=18#

Divide both sides by #2#.

#(cancel(2)^1x)/cancel(2)^1=cancel18^9/cancel2^1#

Simplify.

#x=9#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Solve the second equation:

#-(2x-5)=13#

Expand.

#-2x+5=13#

Subtract #5# from both sides.

#-2x+5-5=13-5#

Simplify.

#-2x+0=8#

#-2x=8#

Divide both sides by #-2#.

#(cancel(-2)^1x)/(cancel(-2)^1)=cancel8^4/(cancel(-2)^1#

Simplify.

#x=-4#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#x=-4,9#